The cyclotron radius rc of an ion with the mass m, the elementary charge e, the charge number z, and the kinetic energy Ekin in a magnetic field of the flux density B is given by the following equation:
                              r          c                =                                            2              ⁢                                                          ⁢              m              ⁢                                                          ⁢                              E                kin                                                          z            ⁢                                                  ⁢            e            ⁢                                                  ⁢            B                                              (        1        )            In the thermal energy range, e.g., at a temperature of 298 K, and in a magnetic field with the flux density of 7 Tesla, the cyclotron radius of a singly charged ion with mass 1,000 dalton is approximately a tenth of a millimeter. Normally, the ICR cell contains a large number of ions, and their masses can be quite different. Before detection, the cyclotron motion of the ions is excited by an oscillating (RF) electric field with a scanned frequency (“Chirp”). When the frequency of the scanned oscillating field becomes equal to the cyclotron frequency
                              v          c                =                              z            ⁢                                                  ⁢            e            ⁢                                                  ⁢            B                                2            ⁢                                                  ⁢            π            ⁢                                                  ⁢            m                                              (        2        )            of an ion with mass m and charge number z, its cyclotron motion gets resonantly excited. In this equation e is the elementary charge. Depending on the duration and the amplitude of the irradiated field, ions become accelerated and move to larger (excited) cyclotron orbits. This resonant excitation also forces ions with the same charge number-related mass (m/z), which initially circle randomly on small cyclotron orbits having completely different phases, to a completely coherent motion. At the end of the excitation process ions with the same charge number-related mass (m/z) form a cloud in which all ions move in phase. Coherently moving ions in this excited cloud induce image charges of the same magnitude at the detection electrodes that oscillate with the same frequency and with the same phase. Such oscillating image charges (image currents) generated by all excited ion clouds are recorded, amplified, and after Fourier transformation displayed as a frequency spectrum or, when a frequency to mass mapping exists, as a mass spectrum.
The magnetic field can only trap ions in the plane perpendicular to the magnetic field lines so that they cannot radially escape the cell. To prevent the ions from escaping in the axial direction, an electric trapping field is required. Therefore, axially, at both ends of the cell, end electrodes (or end plates) are placed on which a relatively low DC voltage (normally, 1-2 volts) is applied. The polarity of this DC voltage is the same as the ions to be trapped. The mantle electrodes of a simple conventional cylindrical ICR cell are grounded, thus, an electric trapping field is formed in the cell between the end electrodes and the cylinder mantle. Ions with the mass m and the charge number z oscillate axially in the cell of the length a between the two end electrodes with a trapping frequency vT if a trapping voltage VT is applied:
                              v          T                =                              1                          2              ⁢                                                          ⁢              π                                ⁢                                                                      2                  ⁢                                                                          ⁢                                      azeV                    T                                                                    m                  ⁢                                                                          ⁢                                      a                    2                                                                        .                                              (        3        )            
Here e is the elementary charge, and α a constant depending on the cell geometry. With this additional oscillation the ion performs a combination of three independent periodic motions in the cell: cyclotron and magnetron motions in the radial plane, and the trapping oscillations in the axial direction.
Although the applied electric trapping field helps keeping the ions from escaping the cell, it definitely deteriorates the conditions for a clean measurement of the cyclotron frequency. Due to the radial components of the trapping field, the ions do not only circle on their pure cyclotron orbits. As a superimposed motion they follow epicycloidal magnetron orbits and they additionally oscillate in the axial direction with the trapping frequency. The magnetron motion is very slow compared to the cyclotron motion. Its frequency only depends on the magnetic field and the electric field. The size (or diameter) of the initial magnetron orbits of ions in the cell right after they are captured depends on how the ions are transferred to the cell: transferred by an electrostatic ion transfer optics or by an RF-multipole transfer optics, or whether or not they are captured using an electric field pulse orthogonal to their path and to the magnetic field (“sidekick”), etc. The initial magnetron radii are normally small, but they can be increased by asymmetric magnetic or electric fields that may excite the magnetron motion. A resistive detection circuit can also induce an increase in magnetron radii due to loss of the potential energy by image current damping.
In the presence of a trapping field, the frequency measured at the detection electrodes of the cell is no longer the unperturbed cyclotron frequency vc but the reduced cyclotron frequency vR:
                                          v            R                    =                                                    v                c                            2                        +                                                                                v                    c                    2                                    4                                -                                                      v                    T                    2                                    2                                                                    ,                            (        4        )            which is smaller by a magnetron frequency vM than the unperturbed cyclotron frequency:vR=vc−vM.  (5)
The magnetron frequency of an ion of cyclotron frequency vc and a trapping frequency vT is:
                              v          M                =                                            v              c                        2                    -                                                                                          v                    c                    2                                    4                                -                                                      v                    T                    2                                    2                                                      .                                              (        6        )            
FIG. 1 shows the combined motion of an ion in an ICR cell in the magnetic field of the flux density B 1. The combination of the cyclotron motion 2, the trapping oscillation 3, of which the sinusoidal curve is shown in dashed lines 4, and the magnetron motion 5 produces the complicated resulting motion 6 of the ion around the electric field axis 7. When an ion is axially introduced exactly in the middle of the ICR cell, it should normally not experience any electric field component perpendicular to its path. The radial components of the electric trapping field are distributed symmetrically around the axis of the DC electric field, i.e., normally around the axis of the cell. Thus, there is no perpendicular electric field component at the cell axis. However, if the electric field axis is, for some reason, displaced and does not coincide with the axis of the cell, a perpendicular electric field component does exist at the cell axis. An ion that is introduced on axis into the cell now experiences this field component, and the influence of the E×B fields immediately diverts it from its initial path. The ion now drifts perpendicular to both the magnetic field and that radial electric field component into the third dimension and starts an epicycloidal orbit that winds on a circle around the offset electric field axis. This is a magnetron orbit with an offset axis in reference to the cell axis. The magnetron radius is basically equal to the displacement of the electric field axis.
FIG. 2a is a partial drawing of a trapping plate 21 of an ICR cell with the ion introduction hole 20. The electric field axis 23 does not coincide here with the geometric axis 30 of the cell, and the radial electric field components 22 make the ion start moving on an epicycloidal 25 magnetron orbit around the electric field axis 23. The virtual magnetron circle 26 is shown in dashed lines. The magnetron radius is here equal to the displacement 27 of the electric field. Element 24 indicates the direction of the magnetic field lines being aligned perpendicular to the plane of illustration.
FIG. 2b shows an electric field axis 23a that is displaced by a much smaller amount 27a than in FIG. 2a. In this case, the ion entering the cell on axis is also influenced by the radial field components 22a and moves on a smaller magnetron orbit 25a around the displaced field axis. The virtual magnetron circle is here also shown in dashed lines 26a and has the same magnitude as the displacement 27a of the electric field. It is to be noted that the displacement of the field axis as well as the complete magnetron orbit 25a remains here within the limits of the ion introduction hole 20 of the ICR cell.
In a trapping field which is asymmetric and not concentric with the cell, severely shifted magnetron orbits can be formed, on which ions can come very close to the mantle electrodes. During a cyclotron excitation on such a shifted magnetron orbit, ions can hit the cell walls and be lost before they are detected.
An asymmetry of the electric field inside the FT-ICR cell can be a consequence of many different effects. Some of them are discussed in the following.
A deviation of individual electrode shapes from the calculated ideal shapes or a deviation of the assembled cell from its ideal shape can cause asymmetry of the electric field inside the cell. Most of the conventional cylindrical cells have only four cell mantle electrodes which are cylindrically bent rectangular electrodes, and their end electrodes are flat circle shaped parts (see 205 and 206 in FIG. 10a). Although these shapes are mostly straightforward, deviations from perfect shapes can still occur if the tolerances are not correctly defined, if the individual electrodes are not cut out of one and the same cylindrical raw material, or if the assembly of the cell is not perfect. In the FT-ICR cells of more complex nature this remains a challenge. Cylindrical cells specially made for high resolution acquisitions contain, for example, more than one detection electrode pair for detection of multiples of the cyclotron frequency. Some of them can have 16 cylinder mantle electrodes which need to be manufactured and assembled within very narrow tolerances. There is a non-zero probability that some individual electrodes of a multitude of mantle electrodes of an ICR cell may deviate to a different extent from the corresponding ideal shape and/or alignment so that the ensuing perturbation of the desired ideal electric field axis could also be non-uniform, for instance, in that a radial shift of the electric field center varies along the longitudinal extension of the cell.
Manufacturing tolerances of parts, as well as deviations from precise assembly in case of compensated cylindrical FT-ICR cells which usually contain 28 or 36 cylinder mantle electrodes (7-section and 9-section cells are known in the art) can influence the electric field symmetry throughout the cell.
Dynamically harmonized cells do have a specially shaped cylinder mantle which usually contains 20 or more cylinder mantle electrodes. If the tolerances of the electrodes are not correctly kept, or if the final assembly of so many electrodes is not perfectly performed these cells are also susceptible to generate electric field errors inside. In a simplest case these field errors can lead to a parallel displacement of the electric field axis from the geometric axis of the cell (uniform perturbation). In more complicated cases, however, these field errors could also lead to at least one of a tilting (the electric field axis and geometric axis of the ICR cell are not parallel any more), a bending (the electric field axis is not a straight line any more, but a non-linear 2D or 3D curve), and a rippling (the electric axis comprises a stepped pattern with abrupt shifts where a perturbation changes significantly) of the electric field axis (non-uniform perturbation).
FIG. 3a shows an example for a dynamically harmonized ICR cell (50), known from the patent application WO 2011/045144 A1 (E. Nikolaev and I. Boldin). This cell has leaf-shaped (e.g. 58) and inverse leaf-shaped e.g., 55, 57, 59, 61 cylinder mantle electrodes. In FIG. 3a, the letter X denotes the cell axis. In order to divide the cell mantle into four equal 90°-segments, four of the eight leaf electrodes are longitudinally divided into two halves e.g., 56a and 56b. Thus the cell has four integral leaf electrodes, four split leaf electrodes, and eight inverse leaf electrodes.
FIG. 3b displays the cylinder mantle electrodes open and unwound. There are two excitation segments E consisting of 5 electrodes 60b, 61, 62, 63, 64a and 69b, 70, 71, 72, 56a. Furthermore, there are two detection segments consisting of 5 electrodes 56b, 57, 58, 59, 60a and 65b, 66, 67, 68, 69a. In the detection segments often only the leaf and half leaf electrodes 56b, 58, 60a and 65b, 67, 69b are used. The inverse leaf electrodes 57, 59, 66 and 68 are normally not used as detection electrodes since these are connected to DC voltage power supplies and thus lead to noisy ICR signals. However, if the DC voltages are generated by a battery, the noise can be avoided, and all five electrodes in a detection segment can be used for signal detection. All inverse leaf plates may be supplied with a common variable DC voltage which normally does not differ too much from the trapping voltage of the end electrodes 80 and 81 of the cell.
Another cause of symmetry errors of the electric field inside the ICR cell may originate from the contact potentials of connectors from the power supply. The contact potentials can change the effective potentials appearing on the individual electrodes, and they can be slightly different from the voltages applied by the user at the instrument console. Depending on the location of these contact potential effects this problem can cause asymmetric electric field inside the cell.
Asymmetric electric fields in the ICR cell can also be a consequence of charging up of individual electrodes. Charging is a general process, which can appear due to various reasons. One of the reasons for electrode charging can be a high resistive connection of this electrode to the ground. Normally, after every acquisition cycle, the detection electrodes in the cell should be at ground potential. However, if they are connected to the ground over a large resistor, which is essential to pick up the extremely low induced image charge signal, this can make it difficult to have a quick and easy discharge after every acquisition cycle. The electrode may maintain its charged state for a while, even after the next acquisition cycle starts. In this way an asymmetric electric field is induced in the cell due to a not-perfectly discharged electrode. Needless to say that this type of charging may manifest itself at different individual mantle electrodes with different magnitudes whereby a non-uniform electric field perturbation along the cell axis may emerge.
A different type of electrode charging is surface charging. This usually happens if the metallic surface of the electrode carries a dielectric layer, which (a) can be polarized or charged and (b) cannot easily be discharged due to its lack of conductance. These non-conductive layers usually appear on electrodes due to chemical contamination of the vacuum system. It is known in mass spectrometry that in contaminated vacuum systems or in the presence of outgassing vacuum components nonconductive layers can be deposited on surfaces of electrodes. This way, the actual voltage at the surface of this electrode can differ from the applied voltage. Applied voltages in the range of 1-2 volts can easily be varied due to surface charging by an amount of 20 to 100 mV, although in selected cases larger values can be observed. Experience shows that such dielectric layers can be dynamic. Depending on their chemical composition they can grow or they can get thinner. Their consistency can even change with time, heat and/or applied chemical “stress” (=additional compounds introduced into the vacuum). As a consequence, the ratio of the applied voltage to the actual voltage of the electrode may change with time.
Contaminations of surfaces can also be caused by ions in the cell, but they can also originate from other sources in the vacuum system, external to the ICR cell. Trapped ions can be the source of the contamination within an ICR cell. Repeated ion ejections in the long term can lead to deposition of substances on the inside surface of the mantle electrodes which form a dielectric layer. An uneven distribution of surface contamination on individual longitudinal electrodes can lead to asymmetric surface charging. As a consequence, a radial displacement of the electric field center can have different magnitudes at different points along the cell axis, which in turn leads to a non-uniform electric field perturbation within the cell. Quenching prior to each acquisition cycle cleans the cell from remaining ions for the next acquisition. During a quench pulse a DC voltage of 20-30 volts of opposite polarity to the trapped ions is applied to one of the trapping electrodes, and as a consequence all remaining ions in the cell are attracted to and hit this electrode. Depending on the compounds being measured, the quench event can also produce a dielectric layer on the inside of this trapping plate, which can then, due to surface charging, deteriorate the axial symmetry of the electric field. It depends on the chemical composition of the contaminant layer whether or not a strong bake-out at e.g. 300° C. eliminates it or if it even strengthens the insulation properties of the layer. Bake-out temperatures are often kept lower (around 150° C.) due to material-related reasons. Thus, the layers may not get completely eliminated. Layers of some specific compositions tend to polymerize at higher temperatures and can sometimes only be removed by mechanic scrubbing.
Contamination sources external to the ICR cell are the vacuum components that, for some reason, cannot be kept clean enough. In many cases external heating jackets used for bake-outs first increase the temperature of the walls of the vacuum chamber. The ICR cell is initially cold, and it gets warmer with some delay depending on the heat transfer coefficients of various components used in vacuum. Due to this delay, contaminants can initially thermally desorb off the vacuum chamber walls, can condense at the electrode surfaces of the cold ICR cell and cause surface charging.